Temporally multiplexed ion-photon quantum interface via fast ion-chain transport

Remote entanglement across distant quantum nodes [1, 2] may be used for long-distance quantum key distribution [3, 4], modular quantum computer architectures [5, 6], as well as quantum enhanced metrology and sensing [7, 8, 9]. Light-matter quantum interfaces are a fundamental building block for such applications, and allow for distributed entanglement between stationary matter qubits by using "flying" photons.

For practical purposes, these quantum interfaces need to be capable of establishing remote entanglement at high rates across a large-scale network of quantum nodes. However, in widely adopted probabilistic schemes based on heralded photon detection [10, 11, 12], it is infeasible to distribute entanglement at useful rates over a few kilometers, as the attempt rate is limited by the round-trip travel-time of photons in a single mode. For example, for a communication distance of 10 km, photon-travel time will be around 100 µs, meaning that the attempt cannot be higher than 10 kHz. In this scenario, even with use of a state-of-the-art photon-matter interface that can yield close to unity photon extraction efficiency [13], the matter-photon entanglement rate beyond tens of kilometers would be limited to sub 10 $\text{s}^{-1}$ with total loss around 15 dB after considering the collective probability of generating and detecting telecom photons at each node, along with the optical fiber loss [14, 15].

A key solution to this challenge is multiplexing: to combine multiple signals into a single channel and therefore increase the attempt rate [16, 17]. Multiplexing has become a mature technology for ensemble-based quantum interfaces, both in atomic gases and rare-earth ion doped solid-state systems [18, 19, 20, 21]. However, large-scale local quantum information processing is technically challenging in these platforms [22].

In contrast, single emitters, including trapped ions and neutral atoms, offer excellent local quantum information processing capability beside their natural interface with light at convenient wavelengths for quantum frequency conversion (QFC) [23, 24], and the possibility of long-lived storage of entanglement [25, 26]. On the other hand, implementing a multiplexed light-matter interface with these systems is technically challenging. Towards overcoming this problem, a few multiplexing schemes have already been proposed for ion and atom-based quantum processors [27, 28, 29, 30]. The only reported experimental work, we are aware of, is the demonstration of multiplexing using a static three-ion chain [15]. In view of the recent advances of the quantum CCD architecture [31, 32, 33], a complementary approach to multiplexing is the process of ion-transport through a specific spatial location with maximized photon coupling efficiency.

In this work, we demonstrate a temporal multiplexing scheme based on the transport of an ion-chain for improving the rate of ion-photon entanglement over long distances. In our experiments, we generate on-demand single photons by shuttling a nine-ion chain across the focus of a single-ion addressing beam. This scheme is expected to lead to a nearly nine-fold increase in attempt rate of the entanglement generation for quantum repeater nodes separated by >100 km. We verify the single-photon nature of the photon trains by measuring a second-order time correlation of $g^{(2)}(0)$ = 0.060(13) without background subtraction. Furthermore, we address the problem of motional excitation during the transport, which is detrimental to local entangling operations [34] and in the case of using a cavity for stimulating the photons would lead to uncertainly in the coupling strength. [35]. Using a shuttling function designed to mitigate motional excitation, we find coherent excitation of $\bar{n}_{\alpha}\sim$ 50 on the center-of-mass (COM) mode during one round of ion chain transport. These results show that the proposed multiplexing scheme can be scaled up to higher rates provided that more optimal transport methods are applied.

The schematics of the experimental procedures is illustrated in Fig. 1(a). Our experiment is conducted using an RF Paul trap, composed of four RF blades for generating radial pseudopotential and two DC endcap electrodes for providing an axial harmonic confinement. We typically trap a string of nine $\mathrm{{}^{40}Ca^{+}}$ ions in a linear configuration with the COM mode frequency of $\omega_{x,z}/(2\pi)=\times$ {1.15, 0.179} MHz and Lamb-Dicke (LD) parameters of the axial modes, ranging between 0.09 and 0.23 on the $4^{2}S_{1/2}\leftrightarrow 3^{2}D_{5/2}$ transition. Two global laser beams at 397 nm and 866 nm (not shown in the figure) evenly illuminate the entire ion chain for Doppler cooling and optical pumping, and a tightly focused addressing beam at 866 nm allows for resonant excitation to extract the 397 nm single photons from individual ions. The generated single photons are collected by an objective with a numerical aperture of NA = 0.3 (collection efficiency $P_{c}\approx 2.5\%$) and directed to a 50/50 beam splitter (BS). At the exit port of BS, photons are detected by two photomultiplier tube (PMT)-based single-photon detectors (SPD), and their arrival times are recorded with a time-tagger for subsequent analysis.

We generate on-demand single-photons based on a background-free scheme, as illustrated in Fig. 1(b) [36]. In this process, we first Doppler cool (detuning $\Delta=-\Gamma/2$) the ion chain for 200 µs, with the first 100 µs assisted by another beam $-500$ MHz detuned from the $4^{2}S_{1/2}\leftrightarrow 4^{2}P_{1/2}$ transition (not shown) to mitigate collision induced ion chain melting in the Paul trap [37]. Then we begin the photon generation sequences with optical pumping to the $3^{2}D_{3/2}$ state for 3 µs, followed by transport of the chain to position each ion in the tight focus of the 866 nm addressing beam resonant with $3^{2}D_{3/2}\leftrightarrow 4^{2}P_{1/2}$ transition to generate 397 nm single photons (see Fig. 1(c)).

In the ion-chain transport process, the endcap voltages are controlled by an arbitrary waveform generator (AWG) amplified by a custom-made, low-noise amplifier circuit with a gain of ten through low-pass filters and a vacuum feedthrough. The low-pass filters have cutoff frequencies of 1.9 MHz to allow fast transport of the ion chain close to the speed of the COM mode frequency. The programmed and the measured waveform show a negligible latency effect from the filters (Fig. 2(a)). The forward shuttling function has eight steps, during each of which a different ion is placed in the focus of the addressing beam for 1.7 µs with the beam turned on simultaneously. After completing this sequence, we move the entire ion chain back to the original position in 35 µs using the same function form in one step. The voltage ramping function on the two endcaps $V_{1,2}(t)$ is in the form of a sigmoid-like polynomial function such that the first and second order derivative at the beginning and the end of the transport vanish [38].

where $\Delta V$ is the voltage difference between the beginning and the end of a step, $t$ is the time after the end of the previous step, and T = 9.1 µs is the total time of each transport. The details of voltage optimization and numerical simulation of motional heating can be found in [39]. We reconstruct the temporal profile of 397 nm photons during transport using the recorded arrival times of photons on the PMTs. Fig 2(b) shows the emission from individual ions (modes). Data is accumulated for 40 min, during which around $1.56\times 10^{6}$ attempts were made to the whole string, corresponding to attempt rate 39.0 kHz, an average photon extraction efficiency of 0.21 % and single photons count rate of around 71 cps.

Next, we perform a two-photon correlation experiment to test the non-classical characteristics of our multiplexed photon source [40]. The probability of two-photon correlation when detecting a correlation event on two detectors at different times is given by

where $\rho_{1}(\tau)$ and $\rho_{2}(\tau+\delta T)$ are the probability of detecting a photon at $t=\tau$ and $\tau+\delta T$ on detector 1 and 2. Fig. 3(a) shows the normalized correlation counts as a function of the delay mode window. We choose a coincidence window of 300 ns in each mode and measure 8 coincident counts at zero delay in 4.8 hours, corresponding to $g^{(2)}(0)$ = 0.060(13). The residual correlation can be explained by excitation of neighboring ions, i.e., crosstalk of the addressing beam, which is separately characterized to be $0.99\,\%$ using fluorescence of the nine-ion chain on the camera, corresponding to expected average $g^{(2)}_{\text{exp}}(0)=0.049(8)$ (see Supplemental [39]). To further verify this hypothesis, we repeat the measurement with a single ion (Fig. 3(c)) and compare it to addressing only the fifth ion in a static nine-ion chain (Fig. 3(b)). The two experiments yield $g^{(2)}(0)$ = 0.010(6) and $g^{(2)}(0)$ = 0.062(17) with 6.0 and 4.8 hours of data accumulation, respectively. While the single ion $g_{2}$ is limited by the detector dark counts and ambient light, the measurement of the static 9-ion chain $g_{2}$ is limited by the crosstalk of the addressing beam. The results indicate the major source of residual correlation is addressing crosstalk [39]. This can be mitigated by coupling the single photons into a single-mode fiber or improving the optical quality of the excitation beam.

After characterizing the single-photon nature of the transport-multiplexing scheme, we characterize the motion of the ions introduced by shuttling. This is important as the quality of subsequent quantum operations on the ions or ion-photon entanglement will depend on the ions’ motional states. We further explore the system performance by measuring the motional heating from the ion transport. To do this, we first perform sideband cooling for all axial modes sequentially using the method similar to that in [41] and prepare the ion in the state $\ket{\downarrow}=\ket{4^{2}S_{1/2},m_{J}=-1/2}$. We compare the $\ket{\downarrow}\leftrightarrow\ket{\uparrow}=\ket{3^{2}D_{1/2},m_{J}=-1/2}$ carrier transition before and after transport with a global 729 nm beam along the axial direction to determine how the transport affects the ion-motion (Fig. 4). The carrier Rabi flopping is motional state sensitive, and the Hamiltonian has the form of [42, 43]

where $\Omega^{(i)}$ is the Rabi frequency of the $i$th ion, $a_{m}$ and $a_{m}^{\dagger}$ are the creation and annihilation operators on the $m$th mode, and $\eta_{i,m}$ is the LD parameter of the $i$th ion and the $m$th mode. Considering the computational difficulty of including all motional modes in the simulation, we only consider the COM mode which we expect to be excited most because the electric fields, both from the transport and surface noise, are correlated over the whole ion string (see Supplemental [39]). Therefore, the average carrier Rabi flopping can be simplified to

where $P_{n}$ is the occupation on the $n$th number state and encodes a convolution between a thermal and a coherent phonon distribution [44]. $\Omega_{n}^{(i)}$ is the Rabi frequency of the $i$th ion on the $n$th number state [45]. To verify the effectiveness of our approximation, we probe the sideband-cooled motional spectrum of the nine-ion chain before the tranport and verify that only the COM mode is not cooled to near the ground state [39], for which we find a cooling limit of $\bar{n}_{th}=4.0\,\pm\,3.0$. We also measure the electric-field noise induced heating and find a heating rate of 20 quanta / ms.(Fig. 4(a)), indicating that the remaining thermal population is likely limited by the COM mode heating which scales as ion number $N$ [46]. Fig. 4(b) shows the carrier Rabi flopping after ion transport twice as slow as in Fig. 2(a). From numerical simulations (blue line), we find that the data can be explained well by a coherent state $\bar{n}_{\alpha}=|\alpha|^{2}\approx 50$ on the COM mode after the transport. Similarly, we perform the full-speed tranport and the carrier Rabi flopping matches with COM coherent state with $\bar{n}_{\alpha}\approx 110$ (Fig. 4(c)). As shown in the Rabi flopping plots, there is mismatch between the experimental data and numerical simulation at full speed, which could be due to thermal and coherent occupation of other modes and will require additional investigation. For example, one can use an individual 729 nm addressing beam to probe the blue sideband transition of different modes [47]. The optimal fast transport of a long ion chain remains an open question and is beyond the scope of this work. However, we note that further optimization can be done by energy self-neutral shuttling [31, 44], implementing closed-loop optimization of the shuttling function [48], etc.

To summarize, we have presented a multiplexed ion-photon interface by transporting a nine-ion chain with synchronized excitation in sub-hundred µs. The speed is restricted by the motional frequency and can be increased by an order of magnitude, for instance, using a 3D-printed ion trap [49] with radial frequency beyond 10 MHz. The 397 nm photon can be converted to the telecommunication band via a two-step QFC [24]. Once integrated with state preparation on $3^{2}D_{3/2}$ Zeeman sublevel and photon collection with a single mode fiber, we expect a faster photon extraction rate [50] and negligible ion crosstalk while achieving high fidelity ion-photon entanglement  [51, 52]. Our system can also be combined with a miniature cavity [35] for much higher photon extraction efficiency without sacrificing the photon generation rate, while the ion’s positional spread caused by coherent excitation can be mitigated by aligning the cavity along the radial direction or further optimization of the shuttling function. These results stimulate the research of fast shuttling of a chain of tens of ions as a unit cell of logical qubit with heralded entanglement [28] and high-rates entanglement of quantum processors across large distances.

B.Y and Q.W have contributed equally to this work. We thank Alp Sipahigil, Ben Lanyon, Tracy Northup, You-Wei Hsieh, and Wenji Wu for their helpful discussion. Q.W. and H.H. acknowledge funding by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Awards No. DE-SC0023277. This work is supported by the Office of Science (S.C.) in Advanced Scientific Computing Research (ASCR) through FOA - Quantum Internet to Accelerate Scientific Discovery (LAB 21-2495) and by NSF Grant No. 2016245.